This invention relates to a system for analyzing and correcting irregular astigmatism to enable surgeons to correct irregular astigmatism in patients and particularly for achieving a symmetrical and orthogonal relationship in two hemidivisions of the cornea of the eye.
The invention also relates to a computer program to analyze irregular astigmatism and provide surgical parameters for correction thereof.
Current methods of analyzing astigmatism are confined to calculation of the vector of change surgically induced in attaining the post-operative result from the pre-operative state.
This ably allows determination of total induced astigmatism and the direction of the vector force acting in the eye. It also enables calculation of the mean total surgical astigmatism induced when a series of operations are compared and analyzed. However, the axes of surgical induced astigmatism (SIA) generally varies considerably within the 180xc2x0 arc of range. This makes it extremely difficult to make meaningful comparisons of astigmatic change for a series, as one cannot obtain an average directional change of vectors, as vectors in opposing or partly opposing directions cancel each other out in varying amounts.
One practice carried out by some surgeons is to resort to the sole option of tabulating each patient""s results individually, leaving it to the reader to estimate any trend. Some surgeons attempt to provide an overview of results, but lack the means to deduce a trend in induced astigmatism vectors as a group, because they have variable orientation.
Taking a mean of the angles has no validity in determining the trend for axes, nor does it address the change in axes from their pre-operative to post-operative astigmatic status. It does not assess the success or desirability of the achieved result; furthermore, it does not indicate the extent to which the surgical aim was achieved. An attempt has been made to address the complexities of correcting the magnitude for the degrees of axis change by introducing the approximation that this component varies as the cosine of the difference between the attempted and the observed (achieved) axes. This corrected value of magnitude was substituted as the amount of surgically induced astigmatism measured on a cylinder 90xc2x0 to the axis of the incisions, the so-called xe2x80x9cproperxe2x80x9d axis. It has been proposed to program so called Naylor""s equations into a computer program that requires slight modifications to resolve the ambiguity and essentially reproduce the Naylor table.
The formula for calculation of SIA is derived from the resultant of two plano-cylindrical lenses with axes at different angles; this was subsequently employed by some surgeons using graphical methods confirming the magnitude and axis of the astigmatic change. Jaffe and Clayman employ rectangular and polar co-ordinates to determine, by vector analysis, the formula for calculating SIA and its axis with the known values for pre- and post-operative corneal astigmatism. Analogous formulae were derived by Hall based on Martin and Welford""s derivation of Euler""s theorem of curved surfaces (investigated by Airy in 1827).
Euler""s theorem, which states xe2x80x9cthat the sum of the curvatures of any two perpendicular sections of a cylindrical or toric surface has a constant valuexe2x80x9d, provides the link between Jaffe""s and Naeser""s methods of vector analysis. Naeser""s method calculates the polar values of astigmatism, arising when the axis of astigmatism does not lie on 90xc2x0 or 180xc2x0 meridia; its use lies primarily in interpreting results of surgery which induces polar (with-the-rule and against-the-rule) changes, such as cataract and implant surgery (with or without transverse astigmatic keratotomy).
Astigmatism is a unique refractive error that causes reduced visual acuity and produces symptoms such as glare, monocular diplopia, asthenopia and distortion. For some years now, astigmatism control and correction has been of great concern to refractive, cataract and corneal surgeons. Reduction or elimination of astigmatism, as a single or combined procedure, is only possible if one possesses an understanding of astigmatic change, in its component parts of magnitude and axis. Current analytical techniques do not allow us to compare magnitudes and axes separately for a series of paired groups of procedures or for a single procedure, yet it is only in this way that we are able to perfect techniques of astigmatism surgery. We need to be able to determine the preferable technique to employ; we also need to be able to determine whether any failure to achieve surgical goals is attributable to an individual patient factor or to machine or technique error. Modern laser technologies have empowered us with the ability to modify our procedures with degrees of sophistication not previously possible; this in turn requires analysis systems which will allow us to accurately quantify and scientifically assess the results.
An object of the present invention is to provide a method which allows more meaningful information to be obtained which can be used by surgeons to provide a greater degree of success when applied to an individual patient and also to provide statistical information which will enable techniques to be improved.
The present invention provides a method of treating astigmatism comprising the steps of:
determining a pre-operative astigmatism;
defining a target or aimed astigmatism;
calculating a target induced astigmatism vector which is the difference between the target astigmatism and the pre-operative astigmatism; and
calculating from the target induced astigmatism vector the direction and amount of relative steepening or flattening of the cornea to provide parameters of a surgical procedure in magnitude and direction.
The target induced astigmatism vector may be modified by an angle of error and a magnitude of error.
The present invention also provides another method of treating astigmatism comprising the steps of:
determining a pre-operative astigmatism; defining a target or aimed astigmatism;
determining an achieved astigmatism following a surgical procedure;
calculating a target induced astigmatism vector which is the difference between the aimed astigmatism and the pre-operative astigmatism, calculating a target induced astigmatism vector which is the difference between the achieved astigmatism and the pre-operative astigmatism, and
calculating a difference vector which is the difference between the aimed astigmatism, and the achieved astigmatism to enable magnitudes of the vectors and angles of the vectors to be obtained.
The present invention also provides another method of treating astigmatism comprising the steps of:
determining a pre-operative astigmatism including a magnitude and axis of astigmatism in a 0xc2x0 to 180xc2x0 range;
defining a target or aimed astigmatism including a magnitude and axis, the axis being an angle presented in a 0xc2x0 to 180xc2x0 range;
determining an achieved astigmatism following a surgical procedure, the achieved astigmatism having a magnitude and axis, the axis being an angle presented in a 0xc2x0 to 180xc2x0 range;
doubling the angles of the axes of the pre-operative astigmatism, target astigmatism and achieved astigmatism to convert the axes to a 360xc2x0 range;
calculating a target induced astigmatism vector which is the difference between the target astigmatism and the pre-operative astigmatism,
calculating a surgically induced astigmatism vector which is the difference between the achieved astigmatism and the pre-operative astigmatism, calculating a difference vector which is the difference between the target astigmatism and the achieved astigmatism, and
halving the angle of the target induced astigmatism vector, the surgically induced astigmatism vector and the difference vector to return the angle values to a 0xc2x0 to 180xc2x0 range and calculating the magnitudes of the vectors to thereby provide astigmatism vector magnitude values and vector angle values.
Since the method produces astigmatism magnitude values and angle values, and in particular a target induced astigmatism vector and a difference vector, results obtained can be used to predict trends in surgery to enable techniques to be improved and also to use particular results for a particular patient in order to surgically correct a previously surgically induced astigmatism to a target induced astigmatism.
Preferably, the step of doubling the vector angles includes the step of converting from polar coordinates to rectangular coordinates.
Preferably, the step of determining preoperative astigmatism comprises making corneal measurements of a patient or, in an alternative embodiment, utilizing information relating to glasses prescription of the patient.
Preferably, the method includes a step of determining a coefficient of adjustment by dividing the target induced astigmatism vector by the surgically induced astigmatism vector.
Preferably, the method includes determining an angle or error and a magnitude of error which are respectively the angle difference and magnitude difference between the surgically induced astigmatism vector and the target induced astigmatism vector.
Preferably, the method includes determining an index of success which is the magnitude of the difference vector divided by the magnitude of the target induced astigmatism vector.
Preferably, the method includes determining an angle of correction which is the angular difference between aimed astigmatism and the achieved astigmatism.
Preferably, the method includes calculating an angle of error which is the angular difference between the surgically induced astigmatism vector and the target induced astigmatism vector.
Preferably, the method includes a step of determining the axis or angle of the difference vector and the magnitude of the difference vector.
Another object of the invention is to achieve surgical correction of astigmatism taking into account differing refractive and topographical measurements of the eye.
Another object of the invention is to achieve such surgical correction so that astigmatism in the eye following surgery when measured topographically and refractively is a minimum. In this respect, when there is a difference between refractive and topographical measurements of astigmatism, surgical intervention considering only one of the above measurements may lead to residual astigmatism following surgery which is worse when measured on the basis of the unconsidered measurement.
The invention satisfies the above object of surgically correcting astigmatism of an eye of a patient taking into account refractive and topographical measurements of the astigmatism by a method comprising:
measuring magnitude and axis of astigmatism of an eye of a patient based on topography of the cornea of the eye of the patient,
measuring magnitude and axis of astigmatism of the eye of the patient based on refractive correction of said eye,
determining surgical parameters based on the measurements of astigmatism both refractively and topographically, and
surgically treating the eye according to said surgical parameters,
said surgical parameters being determined by
a) summating the values of astigmatism measured topographically on the values of astigmatism measured refractively, on the one hand, and the values of astigmatism measured refractively on the values of astigmatism measured topographically, on the other hand, to obtain respective non-zero target astigmatism values for refraction and topography, and
b) establishing said surgical parameters based on both said target astigmatism values such that the sum of the target astigmatism values for refraction and topography is a minimum,
whereby astigmatism in the eye following surgery will be a minimum when measured topographically and refractively.
The step of summating the astigmatism values comprises vectorially subtracting the respective astigmatism values from one another.
A further object of the invention is to provide a method by which an eye having non-symmetrical topography can be treated for astigmatism.
The above object is satisfied by a method comprising:
considering the cornea as divided into two hemi-divisions, and
determining surgical parameters for each hemi-division independently of the other.
Another object of the invention is to provide a method for altering the axis of astigmatism of the eye without altering its magnitude. This is particularly effective according to the invention, to bring hemi-meridians of non-symmetrical topography of an eye into orthogonal correspondence.
The present invention also resides in an apparatus for performing corneal surgery comprising:
means for performing surgery on a patient""s cornea;
control means for controlling the means for performing surgery; and
processing means for receiving said target induced astigmatism vector for the patient and for outputting signals to control the control means in accordance with the target induced astigmatism vector.
Preferably, the means for performing surgery comprises a source of ultraviolet radiation and a shutter device and the control means controls the opening duration of the shutter device and the intensity of the source of ultraviolet radiation.
Preferably, the processing means includes input means for inputting data relating to pre-operative astigmatism of the patient and target or aimed astigmatism so that the processing means can calculate the target induced astigmatism vector.
In the invention described above, an optimal treatment is obtained for the two hemidivisions of the eye, and when the astigmatism is irregular i.e. asymmetrical and non-orthogonal in the two hemidivisions, the optimum treatment vectors TIA in the two hemidivisions are usually unequal in magnitude and non-coincident.
The invention contemplates a second stage in which the treatment vectors for optimal results in the two hemidivisions are combined to provide an orthogonal symmetrical result.
In further accordance with the invention the two stages are performed by a single treatment.